The arrangement was that she was to walk across the moors from the village where they were staying to the Pine Ridge Cafe and go home by bus.
Caesar's Grove is not far from the cafe and it's thought that as she was ahead of time she sat down there to admire the view for a bit before going on, and that some tramp or madman came upon her there and caught her unawares.
Once the husband was proved to be out of it, naturally they connected up her death with that of Nellie Parsons - that rather flighty servant girl who was found strangled in Marley Copse.
They decided that the same man was responsible for both crimes but they never caught him - and what's more they never came near catching him! Drew a blank everywhere."
He paused and then he said slowly:
"And now - here's a third woman strangled - and a certain gentleman we won't name right on the spot."
He stopped. His small shrewd eyes came round to Poirot. He waited hopefully.
Poirot's lips moved.
Inspector Colgate leaned forward. Poirot was murmuring: "- so difficult to know what pieces are part of the fur rug and which are the cat's tail."
"I beg pardon, sir?" said Inspector Colgate, startled.
Poirot said quickly: "I apologize.
I was following a train of thought of my own."
"What's this about a fur rug and a cat?"
"Nothing - nothing at all."
He paused.
"Tell me, Inspector Colgate, if you suspected some one of telling lies - many, many lies, but you had no proof, what would you do?"
Inspector Colgate considered.
"It's difficult, that is.
But it's my opinion that if any one tells enough lies, they're bound to trip up in the end."
Poirot nodded. "Yes, that is very true.
You see, it is only in my mind that certain statements are lies.
I think that they are lies, but I cannot know they are lies.
But one might perhaps make a test - a test of one little not very noticeable lie.
And if that were proved to be a lie - why then, one would know that all the rest were lies, too!"
Inspector Colgate looked at him curiously.
"Your mind works a funny way, doesn't it, sir?
But I daresay it comes out all right in the end.
If you'll excuse my asking, what put you on to asking about strangulation cases in general?"
Poirot said slowly: "You have a word in your language - slick. This crime seemed to me a very slick crime! It made me wonder, if, perhaps, it was not a first attempt."
Inspector Colgate said: "I see."
Poirot went on: "I said to myself, let us examine the past crimes of a similar kind and if there is a crime that closely resembles this one - eh bien, we shall have there a very valuable clue."
"You mean using the same method of death, sir?"
"No, no, I mean more than that.
The death of Nellie Parsons for instance tells me nothing.
But the death of Alice Corrigan - tell me, Inspector Colgate, do you not notice one striking form of similarity to this crime?"
Inspector Colgate turned the problem over in his mind.
He said at last: "No, sir, I can't say that I do really. Unless it's that in each case the husband has got a iron-cast alibi."
Poirot said softly:
"Ah, so you have noticed that?"
"Ha, Poirot. Glad to see you. Come in. Just the man I want."
Hercule Poirot responded to the invitation. The Chief Constable pushed over a box of cigarettes, took one himself, and lighted it.
Between puffs he said: "I've decided, more or less, on a course of action.
But I'd like your opinion on it before I act decisively."
Hercule Poirot said: "Tell me, my friend."
Weston said: "I've decided to call in Scotland Yard and hand the case over to them.
In my opinion, although there have been grounds for suspicion against one or two people, the whole case hinges on dope smuggling.
It seems clear to me that that place, Pixy's Cove, was a definite rendezvous for the stuff."
Poirot nodded. "I agree."
"Good man. And I'm pretty certain who our dope smuggler is. Horace Blatt."
Again Poirot assented. He said: "That, too, is indicated."